Fluid Mechanics
Final Exam
Date: May 28, 2016
Duration: 2 hours
Hodeidah University
Faculty of engineering
Dr. Hasan Maridi
Answer All questions. Useful relations and constants are given in the last page.
Q1- If 5.6m3 of oil weighs 46 800 N, what is
i. the mass (m)
ii. the mass density ()
iii. the specific weight ()
iv. the specific gravity (s.g.)
Q2(a) What happens if the adhesive forces are stronger than the cohesive forces?
(b) The velocity distribution of a viscous liquid (dynamic viscosity = 0.9 Ns/m2)
flowing over a fixed plate is given by u = 0.6y (u is velocity in m/s and y is the
distance from the plate in m). What are the shear stresses ()?
Q3(a) What depth of oil (in m), relative density 0.75, will give a gauge pressure of 275kPa
(b) In a hydrochloric piston of radius 0.5m and 5m for the small and large pistons
respectively. Find the weight and mass of a car that can be elevated if the force
exerted by the compressed air is (F1 = 600N).
Q4(a) What is the absolute pressure in the sea at a depth of 10m?
(b) In figure, fluid 1 is a gas (s.g.=8.6) and the fluid 2 is Benzene (s.g.=15.6). Determine
the absolute pressure at A.
Q5- A manometer is attached to a tank as shown in figure, what will be the difference in
elevation (y) of the mercury column in the manometer.
Q6(a) What is the pressure head, in meters of water, exerted by the atmosphere?
(b) A water pipe of radius 4cm is used to fill a 70liter bucket. If it takes 7min to fill the
bucket, what is the speed at which the water leaves the pipe?
Q7- A sphere block of wood floats in water. The radius of the sphere is 5 cm and the wood
density is 700 Kg/m3. Determine the percentage of the wood, which is not submerged.
Q8- Starting with the Bernoulli and Continuity equations, show that the following
expression gives the discharge measured by a venturimeter.
√
and that when a manometer is attached the discharge may be given by
√
Q9- A large storage tank with diameter of 10m filled with water develops a small hole in its
side at a point 16m below the water level. If the rate of flow from the leak is
2.5×10-3m3/min, determine:
(a) the speed at which the water leaves the hole
(b) the area of the hole.
(c) the time to become the level of the water at the orifice.
Q10- A 50-mm-diameter siphon is drawing oil (s.g.=0.82) from an oil reservoir, as shown
in figure. Neglecting friction, find:
(i) the discharge of oil from the siphon at point 2
(ii) the oil pressure at point 2
Constants, conversion factors, and Useful Relations
The gravitational constant g ≈ 10 m/s2.
1liter = 10-3 m3
3
3
water = 1000 Kg/m , mercury = 13600 Kg/m , air = 1.29 Kg/m3, seawater = 1025 Kg/m3
Newton’s law of viscosity is
where is the shear stress and is the dynamic viscosity
The equation of continuity for fluids: Q=∆V/∆t=Au= constant where u is the velocity.
The pressure P at a depth h in the fluid is given by: P = Patm + g h
The atmospheric pressure Patm = 1 atm = 1.01×105 Pa
For an object with weight Wobj is partially submerged in a fluid of density ρfluid is in static
equilibrium, the buoyant force is given by B = Wobj or ρobj g Vobj = ρfluid g Vdisp
Bernoulli equation:
Flow from a tank with cross section A through an orifice (hole) in the side with cross section
area A0 at a distance h from the surface level. The velocity at the orifice is
and the
√
time takes to fall this height h is
√
√
0
